Inventiones mathematicae

, Volume 163, Issue 1, pp 1–24

Correlations for pairs of closed geodesics

  • Mark Pollicott
  • Richard Sharp

DOI: 10.1007/s00222-004-0427-7

Cite this article as:
Pollicott, M. & Sharp, R. Invent. math. (2006) 163: 1. doi:10.1007/s00222-004-0427-7


In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Mark Pollicott
    • 1
  • Richard Sharp
    • 2
  1. 1.Department of MathematicsWarwick UniversityCoventryUK
  2. 2.Department of MathematicsUniversity of ManchesterManchesterUK